Publication Date:
2021-03-29
Description:
Indicator kriging (IK) is a spatial interpolation technique aimed at estimating the conditional cumulative distribution function (ccdf) of a variable at an unsampled location. Obtained results form a discrete approximation to this ccdf, and its corresponding discrete probability density function (cpdf) should be a vector, where each component gives the probability of an occurrence of a class. Therefore, this vector must have positive components summing up to one, like in a composition in the simplex. This suggests a simplicial approach to IK, based on the algebraic-geometric structure of this sample space: simplicial IK actually works with log-odds. Interpolated log-odds can afterwards be easily re-expressed as the desired cpdf or ccdf. An alternative but equivalent approach may also be based on log-likelihoods. Both versions of the method avoid by construction all conventional IK standard drawbacks: estimates are always within the (0,1) interval and present no order-relation problems (either with kriging or co-kriging). Even the modeling of indicator structural functions is clarified.
Keywords:
Aitchison geometry; Ilr coordinates; Indicator variogram; Logistic regression
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551
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Geosciences; Hydrogeology ; Geotechnical Engineering; Statistics for Engineering, Physics, Computer Science, Chemistry & Geosciences; Math. Applications in Geosciences
Type:
article
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publishedVersion
Format:
application/pdf
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